Spectroscopic analysis of the A and 3 1  + states of 39 K 85 Rb J. T. Kim 1, Y. Lee 2, and B. Kim 3 1 Department of Photonic Engineering, Chosun University. 2 Department of Chemistry, Mokpo National University. 3 Department of Chemistry, KAIST. D. Wang Department of Physics, The Chinese University of Hong Kong. J. Banerjee, E. E. Eyler, P. L. Gould, and W. C. Stwalley, Physics Department, University of Connecticut. Supported by the National Science Foundation, the Air Force Office of Scientific Research, the National Research Foundation of Korea, and KOSEF through NRL in Korea.

Motivations Prior MB + UM − work: Combined analysis of molecular beam (MB) spectra and ultracold molecule spectra based on PA to the 3(0 - ) state (UM − ): → 1 1 , 2 3  +, and b 3  states. MB + UM + + UM – : Incorporating the prior spectra with new ultracold spectra based on PA to 3(0 + ): → the A and 3 1  + states. Previously just a few low-v levels were known. Determine why the A and 3 1 Σ + states are seen in the UM + spectra but not in the UM – spectra. Set the path for future investigations of the extended potential well. Very new: Assignments of excited-state energy levels enable analy- sis of new formation schemes for ultracold ground-state molecules  successful single-laser production of X 1  + (v  =0, J  =0).

Experimental scheme for UM – and UM + (Storrs) (Storrs) 1)PA to form ultracold KRb*. 2)Spontaneous decay into the triplet a 3 Σ + state after PA to 3(0 – ): UM – experiment 3)Spontaneous decay into both a 3 Σ + and X 1 Σ + after PA to 3(0 + ): UM + experiment 4)REMPI detection via intermediate states e(v, J). Ionization Continuum PA SE REMPI X 1  + (v  =0, J  ) a 3  + (v, J) b 3b 3 2 3   e(v, J ) K(4S 1/2 )+Rb(5P J ) K(4S 1/2 )+Rb(5S 1/2 ) 3(0 + ) 3(0 - ) SE

Experimental scheme for MB (Korea) Ionization Continuum MB RE2PI X 1  + (v  =0, J  ) a 3  + (v, J) b 3b 3 2 3   e (v, J ) K(4S 1/2 )+Rb(5P J ) K(4S 1/2 )+Rb(5S 1/2 ) 1)Supersonic beam forms X 1  + with v  =0, 1. 2)REMPI detection via intermediate states e(v, J).

Ionization Continuum PA SE UM RE2PI MB RE2PI X 1  + (v  =0, J  ) a 3  + (v, J) b 3b 3 2 3   e(v, J ) K(4S 1/2 )+Rb(5P J ) K(4S 1/2 )+Rb(5S 1/2 ) Combined UM-, UM+ and MB spectra Intermediate states e(v, J ) can coincide. Comparison facilitates assignments. SE

Excitation windows

Lower energy portion of the MB spectra Energy (cm  1 ) (a) (b) Energy (cm  1 )

Overlapping UM and MB spectra, with assignments MB UM+ UM–

Transition dipole moment calculations by Kotochigova, et al. TDM is very small between v a = 21 of the a 3  + (  = 1) state (which has an outer turning point near 17 Å) and the vibrational levels of the A 1  + (2 1  0 + ) state in our experimental energy region. Transitions to the A 1  + (  = 0 + ) state are much stronger from v  = 89 of the X 1  + (  = 0 + ) state. S. Kotochigova, P. S. Julienne, and E. Tiesinga, Phys. Rev. A 68, (2003).

Effects of the selection rules and transition dipole moments Selection Rule: +  +, –  –, +  –. PA to 3(0 + ): Radiative decay is allowed to the a 3  + (  1) or X 1  + (  =0 + ) states. TDM is large from X 1  + (  =0 + ) to A and 3 1  + (  =0 + ). Transitions are seen to the A and 3 1  + states (UM + ) PA to 3(0 - ): Can decay only to a 3  + (  = 1, 0 – ) not to X 1  +. No transitions to A or 3 1  + (  = 0 + ) from a 3  + (  = 0 – ). TDM is small between a 3  + (  =1) and A or 3 1  + (  = 0 + ). No transitions from a 3  + (  = 1) to the A or 3 1  + states (UM – ) /

Vibrational intervals  G v+1/2 from UM+, UM- and MB spectra Agreement of overall trends with theory shows that the potential energy curves have the correct shape. Some perturbations and scatter are evident, due to admixture between states. Agreement with theoretical  G trends for 3 1   is excellent, even where ion-pair coupling causes anomalous slow rise.

Characterization of the + states at long range Characterization of the A and 3 1  + states at long range Theoretical potentials are shown in Hund’s case (c), with spin-orbit, and in case (a), without spin-orbit. The asymptotic 2(0 + ) state has an avoided crossing near 5.1 Å with 3(0 + ). The 2 1  + state crosses dia- batically with the b 3  state near 5.1 Å. The 3(0 + ) long- range state correlates diabat- ically mostly with the 3 1  + state at short range, after passing through a strong avoided crossing with another 4(0 + ) curve at 7.1 Å.

FCFs between the X 1  + (= 0, 90, and 92) state and the A 1  + () and 3 1  + () states. FCFs between the X 1  + ( v  = 0, 90, and 92) state and the A 1  + ( v ) and 3 1  + ( v ) states. (a) FCFs between the X 1  + (v  = 0, 90, and 92) state and vibra- tional levels v of the A 1  + state. (b) FCFs between the X 1  + (v  = 0 and 90) state and vibrational levels v of the 3 1  + state. In REMPI spectra from high-v  levels of the ground state (used in UM experiments), the FCF distri- bution to levels near the disso- ciation energy limit is broader and has larger FCFs compared to the v  = 0 level (used in MB experiments). (a) (b)

Application: Identifying ultracold molecules in low-levels of the X 1  + state. Application: Identifying ultracold molecules in low- v  levels of the X 1  + state. A long-term goal at UConn has been efficient one-step formation of true ground- state molecules, X 1  + (v  =0, J  = 0). New result: mixed a and X formation following PA to J′=1 of the mixed state 4(1), v′=61 and 2(1), v′=165. Energy levels from the MB + UM + + UM – analysis are used to assign the 1+1 REMPI spectraon. R (Å) PA SE REMPI J. Banerjee, J. T. Kim, E. E. Eyler, P. L. Gould, and W. C. Stwalley, to be published.

REMPI assignments from X 1  + REMPI assignments from X 1  +, v  =0 Blue: X 1  + (v″=0) to 1 1  (v′=0–4) Green: X 1  + (v″=0) to 3 1  + (v′=27–30) Red: X 1  + (v″=0) to 2 3  + (v′=37–43) Detection Laser Wavenumber (cm -1 ) Numerous transitions from X 1  +, v″=0–10 are observed in this spectrum. Roughly 5000 molecules/s formed in X(v″=J″=0) in an ordinary MOT.

Summary New assignments to the perturbed A 1  + and 3 1  + states of 39 K 85 Rb are made by comparing UM +, UM – and MB spectra. Good agreement with potential curves from Rousseau et al. The presence of the 1 Σ + states in the UM + spectra and their absence in UM – spectra can be explained by considering Hund’s case (c) selection rules and TDM calculations. Proposed investigations of the extended potential well by combining the MB and UM spectra. New: one-step formation of X(0,0) by PA in a MOT, identified using these and earlier MB + UM assignments.